Hi Phil,
As a side note, your car is was likely built before '64, if it came with H6 carbs (TRs were registered in the year actually sold, not the year of manufacture).
Triumph used H6s for the first couple years of TR4 produciotin, then began using Zenith Stromberg of their own manufacture. Perhaps an economy move, but also probably in protest of the close relationship between SU and their main competitor. A couple years later Triumph returned to using SUs, this time the HS6 you mention, on TR4A.
The HS6 are shorter-bodied carbs (S=Short), usually fitted to longer manifolds. It's a good setup. I'd personally want to match the H6 to the short TR manifold or the HS6 to the long TR manifold, and not mix them up. There might be some other minor fitting issues, but I'm sure they could be swapped this way, as a set.
To best preserve the value of your car, have you considered getting those carbs rebuilt? Might cost less, too.
I don't think there were any really big improvements to the HS6, over the H6. At least not enough to make a significant difference in performance.
There are several companies rebuilding SUs in the US, and SU parts are being produced again (I believe primarily by Burlen Industries in the UK). Apple Hydraulics is one company doing rebuilds, that I've heard good things about. Their website is
https://www.applehydraulics.com/carbs.htm
I'm sure some others are rebuilding them, and you might do some googling to see what you can find.
However, if you do decide to get newer carbs for your car and want to sell off your old SUs, let me know. I might be interested. My TR4 came with a set of Hitachi SUs from a Datsun 240Z!
Cheers!
Alan Myers
San Jose, Calif.
'62 TR4 CT17602L